scipy.linalg.companion¶

scipy.linalg.companion(a)[source]¶

Create a companion matrix.

Create the companion matrix [R80] associated with the polynomial whose coefficients are given in a.

Parameters:

Parameters:	a : (N,) array_like 1-D array of polynomial coefficients. The length of a must be at least two, and `a[0]` must not be zero.
Returns:	c : (N-1, N-1) ndarray The first row of c is `-a[1:]/a[0]`, and the first sub-diagonal is all ones. The data-type of the array is the same as the data-type of `1.0*a[0]`.
Raises:	ValueError If any of the following are true: a) `a.ndim != 1`; b) `a.size < 2`; c) `a[0] == 0`.

a : (N,) array_like

1-D array of polynomial coefficients. The length of a must be at least two, and a[0] must not be zero.

Returns:

c : (N-1, N-1) ndarray

The first row of c is -a[1:]/a[0], and the first sub-diagonal is all ones. The data-type of the array is the same as the data-type of 1.0*a[0].

Raises:

ValueError

If any of the following are true: a) a.ndim != 1; b) a.size < 2; c) a[0] == 0.

Notes

New in version 0.8.0.

References

[R80]

(1, 2) R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.

Examples

>>> from scipy.linalg import companion
>>> companion([1, -10, 31, -30])
array([[ 10., -31.,  30.],
       [  1.,   0.,   0.],
       [  0.,   1.,   0.]])